# Unified Signature Cumulants and Generalized Magnus Expansions

@article{Friz2021UnifiedSC, title={Unified Signature Cumulants and Generalized Magnus Expansions}, author={P. Friz and Paul Hager and N. Tapia}, journal={arXiv: Probability}, year={2021} }

The signature of a path can be described as its full non-commutative exponential. Following T. Lyons we regard its expectation, the expected signature, as path space analogue of the classical moment generating function. The logarithm thereof, taken in the tensor algebra, defines the signature cumulant. We establish a universal functional relation in a general semimartingale context. Our work exhibits the importance of Magnus expansions in the algorithmic problem of computing expected signature… Expand

#### One Citation

Electron. Commun. Probab. 26 (2021), article no. 12, https://doi.org/10.1214/21-ECP382

- 2021

Generalizing the realized variance, the realized skewness (Neuberger, 2012) and the realized kurtosis (Bae and Lee, 2020), we construct realized cumulants with the so-called aggregation property.… Expand

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